Susie determined that the system of equations below has infinitely many solutions.
The first line goes through the points (2, -13) and (-2, -1).
The second line goes through the points (5, -22) and (-3, 2).
Is she correct? *Use your Desmos calculator
(1 point)
Responses
Yes, Susie is correct.
Yes, Susie is correct.
No, the lines are parallel.
No, the lines are parallel.
She may or may not be correct as the lines possibly cross.
She may or may not be correct as the lines possibly cross.
No, there is no point of intersection.
To determine if Susie is correct, we can graph the two lines and see if they intersect.
Using a graphing calculator or the Desmos calculator, we can plot the points and draw the lines.
The first line passing through the points (2, -13) and (-2, -1) has a slope of (change in y)/(change in x) = (-1 - (-13))/(-2 - 2) = 12/(-4) = -3. The y-intercept can be found by substituting one of the points into the equation y = mx + b, where m is the slope and b is the y-intercept. Using the point (2, -13), we find -13 = -3(2) + b, which gives b = -7.
So, the equation of the first line is y = -3x - 7.
Similarly, the second line passing through the points (5, -22) and (-3, 2) has a slope of (change in y)/(change in x) = (2 - (-22))/(-3 - 5) = 24/(-8) = -3. The y-intercept can be found using the point (5, -22), giving -22 = -3(5) + b, which gives b = -7.
The equation of the second line is y = -3x - 7.
Graphing these two lines on Desmos, we find that they are the same line and they intersect at infinitely many points. So, Susie is correct.
To determine if Susie is correct, we can use the Desmos calculator. We can graph the two equations and check if they intersect at a single point or if they are parallel.
The first line can be represented by the equation:
y = mx + b
To find the slope (m) of the first line, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given points, we have:
m = (-1 - (-13)) / (-2 - 2)
m = (12) / (-4)
m = -3
So, the equation of the first line is:
y = -3x + b
To find the y-intercept (b), we can substitute one of the given points. Let's use (2, -13):
-13 = -3(2) + b
-13 = -6 + b
b = -7
Therefore, the equation of the first line is:
y = -3x - 7
Similarly, we can find the equation of the second line using the given points. The slope (m) is:
m = (2 - (-22)) / (-3 - 5)
m = (24) / (-8)
m = -3
The y-intercept (b) can be found by substituting (5, -22):
-22 = -3(5) + b
-22 = -15 + b
b = -7
Therefore, the equation of the second line is:
y = -3x - 7
Now, we can graph both equations on the Desmos calculator and check if they intersect at a single point or if they are parallel.
To determine if Susie is correct, we can graph the given lines and see if they intersect at a common point or if they are parallel.
To use the Desmos calculator, you can follow these steps:
1. Go to the website: www.desmos.com/calculator
2. In the provided input field, type the first equation in the form of "y = mx + b".
- The first line goes through the points (2, -13) and (-2, -1). To find the slope (m) and y-intercept (b), you can use the slope formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points.
- Using (-13) - (-1) for y2 - y1 and (2) - (-2) for x2 - x1, you can calculate the slope m = (-13 - (-1)) / (2 - (-2)) = (-12) / (4) = -3.
- To find the y-intercept b, you can substitute one of the given points into the equation. Using (2, -13), you get -13 = -3(2) + b. Solving for b, you get b = -7.
- The equation for the first line is y = -3x - 7.
3. Type the equation into the input field and press the "+" button to add another equation.
4. Repeat steps 2 and 3 for the second line, which goes through the points (5, -22) and (-3, 2).
- The slope can be calculated as m = (-22 - 2) / (5 - (-3)) = (-24) / (8) = -3.
- Using (5, -22) in the equation, you get -22 = -3(5) + b, which gives b = -7.
- The equation for the second line is also y = -3x - 7.
5. After adding both equations, the Desmos calculator will automatically graph them.
6. Look at the graph to see if the lines intersect or if they are parallel.
If the lines intersect at a common point, then Susie is not correct, and the system of equations has only one solution. If the lines are parallel, then Susie is correct, and the system of equations has infinitely many solutions.